A 3-connected matroid M is sequential or has path width 3 if its ground set E(M) has a sequential ordering, that is, an ordering (e1, e2, . . . , en) such that ({e1, e2, . . . , ek...
A minimal k-cycle is a family of sets A0, . . . , Ak−1 for which Ai ∩ Aj = ∅ if and only if i = j or i and j are consecutive modulo k. Let fr(n, k) be the maximum size of a ...
We sharpen a result of Hansel on separating set systems. We also extend a theorem of Spencer on completely separating systems by proving an analogue of Hansel’s result.
We present various techniques to count proportions of permutations with restricted cycle structure in finite permutation groups. For example, we show how a generalized block theo...
In a paper of Klazar, several counting examples for rooted plane trees were given, including matchings and maximal matchings. Apart from asymptotical analysis, it was shown how to...
We investigate the historical roots of the field of combinatorics on words. They comprise applications and interpretations in algebra, geometry and combinatorial enumeration. The...
3 We define four families of geometries with as point graph the graph — or its complement — of all elliptic 4 hyperplanes of a given parabolic quadric in any finite 6-dimensi...